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HalfEarth

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Measurement in Half Earth
Half Earth takes place in a different universe, and is a science fantasy, rather than pure science fiction or fantasy. We know fantasy universes tend to use the imperial system (except some anime chose metric because that's what Japan uses) while science fiction tend to use metric and even Planck units. As a compromise, I created a fictional unit system based on some of the made-up units from my high school chemistry exams, and attached SI prefixes into front of them.

Here is my work-in-progress measurement and timekeeping systems, which might contain calculation and scaling errors.

The unit for length is narl (n). An average person is 3 to 4 narls tall.

The unit for mass of thud (t). An average human weights 150 thuds, and a typical car weight in the range of 2 kilothuds. 

Time is measured in seconds (s), minutes (min) and hours (h), like in our world.

The three units above are the basis for the NTS system, and the derived units are based on powers of them.

The most common way to measure speed for cars is kilonarls per hour (kn/h). Don't be surprised by the large numbers in the speedometers. The typical highway speed (and the reference to measure car acceleration) is 200kn/h, and the typical top speeds for high-end (but not top-end) racing cars is 500kn/h.

From the theory of elliptic relativity, everything are traveling at the constant speed in spacetime at about 8Mn/s.

The unit for volume, is cubic decinarls, or "cd". That's the scale of cups and bottles.

The acceleration due to gravity on Half Earth is 18 n/s^2.

Energy is measured in energy units (EUs). One EU equals to (1 t n^2/s^2). The unit for power EU/s.

Date and Time in Half Earth

In ancient Half Earth, there is the agricultural calendar, which divides a year into four seasons: spring, summer, fall and winter. Each season is about 90 days and there was no predictable pattern for the lengths of each season: They range from 80 to 100 days, and the exact length of them vary by region (about 5 in total): The length of a season depend on both local climate conditions and even political needs. In Half Earth, a year is 360 +/- 1 days long.

The switch to the business calendar marked the beginning of the modern era of Half Earth. After the three empires dissolved, and the world opened up, calendar reform became important for global communication. The reformed calendar was used to be called as "astronomical calendar", "rational calendar" and "revolutionary calendar", but many people called it business calendar by the year of 1000. The business calendar knows nothing about seasons, and it divides a year into quarters of 89 to 91 days, and the lengths of the years are decided by the Earth's position relative to the fixed stars in the celestial sphere. When the "astronomical calendar" was created, astronomers need to predict the lengths of the next four quarters. By year 850, it has been found that the length of a year is precisely 358.8 +/- 0.01 days (accurate to milliseconds by year 1050) and a predictable system of quarters has developed: For the last digit of year, the length of each quarters (Q1, Q2, Q3, Q4) are:
0: 89, 90, 90, 89
5: 90, 90, 90, 89
1, 6: 89, 90, 90, 90
2, 7: 90, 89, 90, 90
3, 8: 90, 90, 89, 90
4, 9: 90, 90, 90, 89

With the system above, the position of Earth's orbit leads by one day behind every 100 years, which means, for every year ending with 00, the length of Q2 is 89 days. With this compensation in place, the a year lags behind by 1 day approximately every 700 years.

The standard date format of business calendar is roughly {year} Q{quarter} (D|-){day}. For example, year 1050, quarter 1, day 5 are often expressed as 1050Q1-5, 1050-1-5, with or without a 0 before 5. When spoken, the day is referred as "the Nth" rather than "day N". In English, the order is often reversed as day-quarter-year or quarter-day-year.

Weeks in Half Earth
In Half Earth, a week is 10 days, and the days are referred by their ordinals starting from one: day 1, day 2, ... day 10. The days 5, 9 and 10 are the non-working days. Day 5 is called the "midweek" and the last two days "weekends". Some institutions practice in the "rotating weekends" system, where two non-working days are distributed between the days 9, 10, 1, 2, and at any given day, there is at least one third of Earth in working day.
Real roads
Real traffic
Virtual Racing
This is Street View Racing

Street View Racing is a virtual reality racing game taking place on the real-time digital representations of the real world. The hardware of the game are often custom-built simpits resembling mid 21st century cars. In Street View Racing, the player drives a car virtually located in a real-world road. SVR virtual cars can collide into buildings, terrain and even real-time traffic. However, real-time traffic cannot be knocked by virtual cars, of course.

Street View Racing is not only virtual reality, but also contains augmented reality elements. Street View Racing sessions can be viewed from the real-world location the virtual cars are present.
First, I need to begin with a correction. In the first article I said gravity in the Half Earth universe is inverse cube in four dimensional spacetime, and to approximate the gravitational force the Earth exerts on an object at any given point in time, we need to integrate the 4-dimensional gravitational force from Earth from the past to the future. In spacetime, the Earth is a curve embedded in four dimensions. We can approximate the Earth's trajectory with a line, and the integral will be similar to electric field generated by an infinite line of charge, except it's done in 4 dimensions and the power is changed from 2 to 3. At that time, either I didn't set up the integral properly or I did the integral wrong, and I concluded gravity in three dimensions is inverse cube, and as a consequence, all orbits will look like Cotes' Spiral.

Recently, I set up the integral again, with care taken over the normalization of 4-dimensional vectors, and I concluded the approximation of gravity is actually inverse square! In other words: In the Half Earth universe, gravitational force is inverse cube in 4 dimensions, but because an object receives gravitational force from the past and future, the classical approximation of gravitational force is actually inverse square. So I need to rewrite some parts of Half Earth astronomy.

The Half Earth universe is a 4+1-dimensional universe with 4 dimensions of spacetime and 1 dimension of metatime. In our universe's spacetime, we change between inertial frames of reference using the Lorentz transformation, where space and time is transformed by a hyperbolic rotation (using sin and, cosh), and the Lorentz transformation preserves causality. In the Half Earth universe, frame of reference transformation is done by doing a conventional rotation (using sin and cos), we call it angular transformation.

Finally, don't forget about the Galilean transformation, where frame of reference transformations only shear the position component while leading time intact.

Galilean
  • Simultaneity: same
  • Distance: same
  • Time interval: same
  • Interval: ds^2 = dx^2 + 0*dt^2
  • Causality: preserved
  • Constant-acceleration trajectory: parabola
  • Rotation: Shear
    • Matrix: [[1 v] [0 1]] = exp(v*[[0 1] [0 0]])
    • Angle: v = v
    • Trig: opposite=v, adjacent=1
    • Algebra: dual numbers (i^2 = 0)
Lorentz
  • Simultaneity: leading clock lags
  • Distance: shorter
  • Time interval: shorter
  • Interval: ds^2 = dx^2 - dt^2
  • Causality: preserved
  • Constant-acceleration trajectory: hyperbola
  • Rotation: Hyperbolic
    • Matrix: [[cosh(beta) sinh(beta)] [sinh(beta) cosh(beta)]] = exp(beta*[[0 1] [1 0]])
    • Angle: tanh beta = v
    • Trig: opposite=sinh beta, adjacent=cosh beta
    • Algebra: split-complex numbers (i^2 = 1)
Angular
  • Simultaneity: leading clock leads
  • Distance: longer
  • Time interval: longer
  • Interval: ds^2 = dx^2 + dt^2
  • Causality: not preserved
  • Constant-acceleration trajectory: elliptical arc
  • Rotation: Circular
    • Matrix: [[cos(theta) sin(theta)] [-sin(theta) cos(theta)]] exp(theta*[[0 1] [-1 0]])
    • Angle: tan theta = v
    • Trig: opposite=sin theta, adjacent=cos theta
    • Algebra: complex numbers (i^2 = -1)

A universe with angular relativity will have relativistic effects opposite to our universe's Lorentz relativity. In our universe, time pass slower for moving objects, and in Half Earth universe, time pass faster for moving objects. In our universe, leading clocks lag, and in Half Earth universe, leading clocks lead. Finally, in Half Earth universe, moving objects are longer, rather than shorter.

The most striking differences between Lorentz transformations and angular transformation are (1) speed of light and (2) causality. In our universe, the light cone divide our hyperbolic space into spacelike and timelike regions, and the light cone imposes the cosmic speed limit and prevents sequences of events from reversing themselves.

In angular relativity, there is no cosmic speed limit: You can get faster and faster forever, but as you accelerate, something strange happens: your speed will approach infinity relative to rest frame, and then you can travel back in time! In other words, you are moving "backward" in time relative to a stationary observer: that is time travel. Since you are time traveling, the station observer can see TWO copies of you, one traveling forward in time and one backward in time. You can even go in circles and meet you in the past, of course. The conversion factor between distance and time unit is called c, and coincidentally, it is the launch speed of some small subatomic particles including light (many particles are launches 45 degrees away form source in space-time diagrams).

Time traveling leads to paradoxes, but there is a solution: The universe is self-adjusting over the 5th dimension called metatime. As metatime passes, the paths of the particles will adjust themselves so they approach the paths of least action. If we look at conservative forces where force = -grad potential, then a physical system's metatime evolution can be described as derivative (position over metatime) = -constant * ( force + grad potential ). The metatime differential equation follows the principle of relativity: It is true no matter what angular transformation (rotating in four dimensions, and picking an origin) you perform on the physical system.

The self-adjusting process may not be totally stable: That means, the universe is constantly adjusting paths of particles, but it can never reach a stage where no further adjustments can be made, even with the absence of time travelers.

Picture yourself flying from Vancouver, Canada to a business meeting in Chongqing, China beginning from leaving your apartment to the meeting site. Here is a wordy description: Before you leave the building, you need to take the elevator. Stairs are too slow and tedious. After leaving the building, you called the taxi to get to the airport: You don't use public transit because you can't afford to wait for buses and you can't handle baggages in crowded spaces.

You don't take the train because they can't travel across the ocean. You don't go on ships because they are too slow. However, you don't get into a fighter jet because supersonic speed is overkill and fighter jets require expensive maintenance after each flight (I think). Commercial airlines are fast and efficient enough, and it has been optimized over and over again to carry many people at a time.

Before you board the plane, you go through the pipelines of checkout, security, baggages, waiting. Wait, I forgot to mention that there's no direct flight from Vancouver to Chongqing, instead, you first fly to Beijing then take another flight to Chongqing.

After you landed in Chongqing, you are still 50km away from the meeting site: Another taxi ride to the front door of the building, and then another elevator ride to the exact floor of the meeting room.

Now here's a more concise, but science fictional example that explains transportation hierarchy: Suppose you are living in an interstellar civilization and you want to take a relativistic flight from a Martian colony in the Sol system to a lunar colony in Alpha Centauri:
 - You go to the airport and ride a plane to the equator
 - Then you take the shuttle to high Mars orbit (space launches are cheaper in the equator due to planet rotation)
 - You arrive at a space station, and you ride a bigger ship to escape from Mars and head to the interstellar shipyard between the orbit of Jupiter and Saturn (It takes months to years)
 - You board the relativistic spacecraft, and depart to Alpha Centauri. In the initial acceleration phase, the ship gets accelerated by a megastructure that emit lasers

Now let's think about faster-than-light travel in science fiction: Ever heard of a FTL drive (that's not teleportation or wormholes) that allows you to fly from your house to your friend's house in a distant colony light years away?

The theory of transportation hierarchy is what 22C urban planners subscribe to. It is first developed by a Russian author in late 21C in the book "Travel Fast, Travel Slow: The Theory Behind Getting from Point A to Point B" (erroneously referred as "[The Theory] of Transportation Hierarchy"). Transportation hierarchy is based on the common sense that one does not ride a fighter jet to get to school. Transportation hierarchy is applicable to scales from small villages to interstellar civilizations. Transportation hierarchy is about the traveling over a short or long distance while trading off between energy and time, just like memory hierarchy is about storing and retrieving a little or a lot of data while trading off between cost and speed.

A transportation hierarchy is a system of ways to get from point A to point B. The hierarchy center around three concepts: distance (or speed), organization and means of transportation. On the top of the hierarchy, larger distances are covered, on the top of geographical organization, and the means of transportation are high-speed and tend to travel in straight lines without stopping. If Earth is the top of the transportation hierarchy, then spacecrafts and long-range aircrafts are the means of transportation that dominate this level. As we move down the hierarchy (state, province, city), the distance covered decrease (50Mm, 1Mm, 100km), the speed decrease (500km/h+, 150km/h, 80km/h). When we reach sub-city levels, we start to deal with moving with cars, public transit or on foot, and the tradeoffs between point-to-point (cars) and spoke-hub (public transit).

Here is a summary of levels of transportation hierarchy, real and science fictional:

Galactic: 10000ly, FTL travel, most paths need straight lines
Interstellar: 100ly, relativistic travel, it's important to start far from the gravity well
Solar system: 10AU, transfer orbits, it's important to carry less mass, time launches well and start higher from planetary gravity wells
Planetary orbit: 1Gm, transfer orbits, it's more useful to measure gravitational potential difference or delta V than distances

International flights: 10Mm
Domestic flights: 5Mm, some common international paths are be point-to-point, while most possible international parts require transfer to hubs

Provincial: 1Mm, Flights or highways depending on the traveller's needs
City, district: 50km (commuting), public transit should cover more possible paths, and for cars, congestion waste time and fuel, cars should approximate the straight line from A to B

Neighborhood: 3km (walking), everything should be within walking distance, but unlike cars, stopping and turning are not burdens
Building: 80m, elevators for tall buildings

Floor: 30m
Room: 4m

An effect of having transportation hierarchy is that the time to get from point A to point B can potentially depend on how many levels traversed, not the distance of the shortest path from A to B. Another way to see it is that negligible distances (for example, the 30km drive to the airport for a 1000km flight) during a trip might not translate to negligible times (the 30km drive and the check-in will take 2 hours, compared to the 2-4-hour flight).

The tradeoffs between point-to-point and spoke-hub, on top of the need to save the environment, are the most visible applications of transportation hierarchy. 22C urban planning involve balancing these factors by artificially constructing levels of transportation hierarchy:
 - Speed (walking vs. riding vehicles)
 - Energy efficiency
 - Scalability and throughput (transportation for a family vs. transportation for a city)
 - Cost
 - Flexibility (Point-to-point vs. hubs)

The means of transportation that dominate city-scale are trains, cars and feet, but by changing the structure of roads they travel on, their parameters will change radically.

To make cars travel faster (save time) and stop less often (save energy), 22C urban planners managed to design roads to make cars travel at highway speeds in almost-straight lines more often. Three-dimensional road layouts are what 22C cities can have. The tradeoff is that cars stop at large parking lots below blocks (22C definition: an area of at most 20-30min walking distance) and people need to walk to the precise destination.

To pack more people per square meter, 22C cities are also built to be tall. Skyscraper apartments are common. The elevator is the vertical counterpart of the car, since an elevator, like a car, covers a long distance in short time. The gain for adding elevators is limited. The first optimization is to let passengers enter the destination before stepping into the elevator and the elevator software intelligently schedule the floor to stop at. However, the most radical change 22C architects came up with is the so-called "serial-parallel configurations". In serial-parallel configurations, more elevators are added without increasing the floor areas elevators occupy. The conceptually simplest way to achieve that is to add more independent elevators per shaft. However, the way to solve the problem with transportation hierarchy is to artificially introduce levels of transportation hierarchy.

Let's say there is a 300-floor skyscraper. We can divide the 300 floors into ten 30-floor floor groups. For each floor group, the lowest floors in the group are the master floors for each floor group. There are a few central high-capacity elevators (master elevators) that only stop in the master floors (the vertical counterpart of public transit). For floors within the floor groups, there are elevators that span only within the floor group. Variations include more floor group subdivisions. (The optimal number of floor group subdivisions and what should be in each subdivision is a computational problem)

See also: gizmodo.com/5905096/the-postal…
In the Half Earth universe, magical power is limited to certain groups of humans and aliens: In the Age of Three Empires, only the Jali Empire has magic integrated to all aspects of their culture, to the extent magic can replace technology and become weapons. There was a controversy over whether magic is innate to all humans (and a magic-enabled culture is required to unlock the potential), or innate to a limited number of races (for example, the citizens of Jali (Jalians)). Magical powers were observed in the non-magical cultures, but they were not recognized as magic and they were called "psychic power", "neigong", until scientists discovered the biological basis of magic.

During the Age of Three Empires, the controversy was only a secret knowledge, of the so-called Outliers, who can take command all three of magic, martial arts and technology. Research over this topic were also done by several militaries in order to create super-soldiers.

In the Post-Empire Age (tech level equivalent of our Earth's 2020), the former empires retained their cultured, therefore their specializations (magic, martial arts and technology). With freer flow of ideas, members of non-magical cultures began to find ways to gain magical powers. That was when the problem of "Is magic innate?" became known to everyone.

In the next century, scientists scrambled to uncover the biological basis of magic: They realized magical energy is part of every human's body, but the potential to control and amplify magic (powerful enough for combat and replace most technologies) has strong genetic basis. After the conclusion became public, non-post-Jalians suddenly wanted to find Jalians as mates. The future will be the universal access of magical powers.

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:iconbellcain:
BellCain Featured By Owner Apr 30, 2015  Hobbyist Traditional Artist
Thanks :D
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LunarSkyes Featured By Owner Apr 26, 2015  Student General Artist
Thank you for the favourite :D
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Zodler Featured By Owner Mar 15, 2015
Need more fion
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MadameAngelDoll Featured By Owner May 8, 2014  Hobbyist Digital Artist
Thanks for the :+devwatch: :D
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kitsunetwo Featured By Owner Mar 13, 2014  Hobbyist General Artist
Thank you very much for the fav Kudryavka Noumi (Smile) [V1]
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Elekitelik Featured By Owner Mar 7, 2014  Hobbyist Digital Artist
Thank you so so much for the fav on my Abby Naruto!!! I really appreciate it a LOT!!! :D :love: :love:
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Pipster61 Featured By Owner Feb 11, 2014  Hobbyist Traditional Artist
thanx for the share and fav :)
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KinduhSortahMaybe Featured By Owner Jan 24, 2014  Student Digital Artist
Thanks for the watch! Bunny Emoji-26 (Teehee) [V2] 
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maskedpeach Featured By Owner Jan 19, 2014  Hobbyist
thank you very much for the watch!:iconahehplz:
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MumiTomoe Featured By Owner Jan 7, 2014
Thx for the Llama.
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